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-(b + a*x - 2*Sqrt[b + a*x] - 2*(-1 + b + a*x)*Log[1 + Sqrt[b + a*x]])/(2*a)


Integrate[Log[1 + Sqrt[b + a*x]], x] ==
-(b + a*x - 2*Sqrt[b + a*x] - 2*(-1 + b + a*x)* Log[1 + Sqrt[b + a*x]])/(2*a)



Integrate[Log[1 + Sqrt[b + a x]], x] == 

-(b + a x - 2 Sqrt[b + a x] - 
 
     2 (-1 + b + a x) Log[1 + Sqrt[b + a x]]) / (2 a)

Time to compute: 0.05 second

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